This invention relates generally to the field of geologic modeling. More particularly, the invention is a process for constructing a three-dimensional (3-D) geologic model of a subsurface earth volume in which the positions of geologic interfaces within the model are adjusted as the model is being constructed in order to improve the consistency between the model and available geologic and geophysical information regarding the subsurface earth volume.
Geologic Modeling in General
In the oil and gas industry, geologic models are often used to aid in activities such as determining the locations of wells, estimating hydrocarbon reserves, or planning reservoir-development strategies. A geologic model is a computer-based representation of a subsurface earth volume, such as a petroleum reservoir or a depositional basin.
Geologic models may take on many different forms. Most commonly, descriptive or static geologic models built for petroleum applications are in the form of a 3-D array of model blocks (cells), or less commonly discrete model points, to which geologic and/or geophysical properties such as lithology, porosity, acoustic impedance, permeability, or water saturation are assigned (such properties will be referred to collectively herein as xe2x80x9crock propertiesxe2x80x9d). The entire set of model blocks constitutes the geologic model and represents the subsurface earth volume of interest. Each model block represents a unique portion of the subsurface, so the model blocks should not overlap each other. Dimensions of the model blocks should be chosen so that the rock properties within a model block are relatively homogeneous, yet without creating an excessive number of model blocks. Most commonly, model blocks are square or rectangular in plan view and have thickness that is either constant or variable, but any shape may be used.
A geologic model is generally constrained by stratigraphic or structural surfaces (e.g., flooding surfaces, sequence interfaces, fluid contacts, faults) and boundaries (e.g., facies changes). These surfaces and boundaries define regions within the model that possibly have different rock properties. The term xe2x80x9cgeologic interfacexe2x80x9d will be used herein to refer to any interface between two subsurface regions having potentially different rock properties, including but not limited to structural and/or stratigraphic surfaces, facies boundaries, and the like.
In the geologic-modeling process, geologic interfaces are generally interpreted and positioned with the aid of well and seismic data, and are integrated into the geologic model as surface grids, polygons, or in other forms. Typically, these geologic interfaces are fixed within the geologic model; therefore, negligible uncertainty in their position is assumed. If this assumption is wrong, i.e., if the positions of geologic interfaces are inaccurate, the resulting geologic model may be a poor representation of the subsurface earth volume of interest. Moreover, the fact that the model is inaccurate may not be apparent to the persons who constructed it. Use of an inaccurate model could be very costly, potentially resulting, for example, in inaccurate estimates of hydrocarbon reserves, missed hydrocarbon-reservoir targets, and inappropriate reservoir-development strategies.
To minimize the risks associated with inaccurate positioning of geologic interfaces, an effort should be made to ensure that the positions of the geologic interfaces within the model are consistent with all available information and target assumptions for the subsurface volume being modeled. For example, the positions of geologic interfaces in the model should be consistent with all available seismic and well data, and with target assumptions such as frequency distributions for rock properties within regions defined by the geologic interfaces. Such efforts to ensure consistency are rarely pursued, however, as they can be expensive, time consuming, and subjective.
The goal of the geologic-modeling process is to assign rock properties to each model block in the geologic model so that the resulting model is an accurate representation of the subsurface earth volume of interest. This process can use many different data types, including but not limited to rock-property data obtained from wells, seismic data, structural and stratigraphic surfaces in the form of 2-D computer grids or meshes, and polygons or polylines that define distinct regions within the model. The latter two data types are described in more detail below.
The geologic-modeling process uses these data to assign values of the rock properties of interest to all model blocks within the geologic model. The assignment of a rock-property value is a process known to persons skilled in the art of geologic modeling. The value that is to be assigned to each model block is calculated using one of many known estimation methods, though the most commonly used methods are geostatistical.
Geostatistical estimation methods (which may be either deterministic or probabilistic) take into account distance, direction, and spatial continuity of the rock property being modeled. Deterministic estimation methods calculate a minimum-variance estimate of the rock property at each block. Probabilistic estimation methods develop distributions of the rock-property values and produce a suite of geologic models for the rock property being modeled, with each model theoretically being equally probable. The spatial continuity of a rock property may be captured by a variogram, a well-known technique for quantifying the variability of a rock property as a function of separation distance and direction.
Model-Based Seismic Inversion in Geologic Modeling
There are many procedures for constructing geologic models. The preferred geologic-modeling procedure for use with the present invention is referred to herein as xe2x80x9cmodel-based seismic inversion.xe2x80x9d Model-based seismic inversion requires that numerous synthetic seismic traces be generated by perturbing model parameters (e.g., rock properties), until there is reasonable agreement between these synthetic seismic traces and actual seismic data traces for the subsurface volume being modeled. Obviously, the synthetic seismic traces should represent the type of actual seismic data being used (e.g., full stack, near-offset stack, far-offset stack, etc.).
Synthetic seismic modeling typically applies a convolutional modeling process. This process consists of using acoustic-impedance values (the product of acoustic velocity and density) to calculate reflection coefficients at the interfaces between layers in the model, and then constructing synthetic seismic traces by convolving the reflection coefficients with a specified seismic pulse. Model-based seismic inversion methods typically are constrained by various conditions that control the outcome. For example, the model may be constrained by measured acoustic-impedance data at wells and by stratigraphic surfaces interpreted in the seismic data. These constraints provide stabilization in the presence of seismic noise and reduce the number of possible solutions.
Some model-based seismic inversion approaches use geostatistical algorithms, such as sequential Gaussian simulation and sequential indicator simulation, to simulate reservoir properties (see e.g., Debeye et al., xe2x80x9cStochastic inversionxe2x80x9d, The Strategic Importance of Oil and Gas Technology, Proceedings of the 5th European Union Hydrocarbon Symposium, Edinburgh, U.K., 1997, v. 1, p. 166-175 and Debeye et al., xe2x80x9cMethod for estimating or simulating parameters of a stratum structurexe2x80x9d, European Patent Application No. EP 0 864 882 A2, published Sep. 9, 1998). The simulated values are systematically perturbed until a synthetic seismic trace calculated for a particular location within the model matches the observed seismic data trace for that location. This process is repeated until all traces are matched.
U.S. Pat. No. 5,838,634 describes a similar model-based inversion approach, except that geostatistical algorithms are not used in the geologic-modeling process. Rather, a simulated-annealing algorithm is used to assess not only the match between the synthetic seismic traces and the actual seismic traces, but also the match between (1) statistics that describe the distribution of rock properties within the geologic model, and (2) other specified geological and geophysical criteria. Such criteria could include lithofacies proportions, histograms of porosity by lithofacies, 3-D measures of lithofacies and porosity continuity (variograms), etc. The match between the statistics calculated for the tentative model and the geological and geophysical criteria is assessed, and the rock properties assigned to each block in the model are perturbed until there is a match within specified limits.
In the procedures described above, as with most geologic-modeling procedures, the geologic interfaces used in constructing the models are fixed, i.e. they are not perturbed during modeling. Thus, if the geologic interfaces are positioned inaccurately, the resulting geologic model will likely be an erroneous representation of the subsurface earth volume of interest.
Geologic Interfaces that Define Zones and Regions in the Subsurface
Structural and stratigraphic surfaces are important features of the earth""s subsurface. These geometrical entities represent the results of tectonic and depositional processes that are important for development of the geologic conditions in the subsurface. Surfaces are also important for geologic modeling. The geologic surfaces are pictured in the form of contour maps, and are estimated and represented by computer grids generated by computer programs. A computer grid or surface typically consists of a series of (X, Y) locations, with one or more depth (Z) or time (T) values assigned to each location. These (X, Y) locations are referred to as xe2x80x9cnodes.xe2x80x9d The nodes may form an ordered array (e.g., a pattern of equi-dimensional rectangles) or a set of complex shapes (e.g., a pattern of space-filling quadrilaterals of varying sizes and shapes, or sets of Delauney triangles). Various computer programs are available to generate such computer grids using data interpreted from wells, seismic surveys, or other sources.
Computer grids influence generation of most 3-D geologic models. Such grids describe the top and base of the model, thereby defining the volume of rock that constitutes the model. Grids are also used to define subintervals within the model that represent different layers (e.g., formations). Computer grids typically are used to define stratigraphic correlations within the model, that is, the grids indicate the depths at various locations that represent the same geologic time or depositional event.
Two surfaces that are stratigraphically adjacent to each other define an interval, one surface representing the top and the other the base of the interval, hereinafter referred to as a xe2x80x9czone.xe2x80x9d A geologic model may have a single zone, but more commonly models consist of several zones, each defined by gridded surfaces. The top of one zone typically is defined by the same grid as the base of the overlying zone. Because the zones in a model are deposited under different geologic conditions, it is likely that rock properties differ between zones.
In nature, surfaces intersect each other. For example, an unconformity is an erosional surface that truncates underlying surfaces. Such intersections must be incorporated into the computer grids used for generating 3-D geologic models. Stratigraphic relations that are commonly used in geologic modeling are conformity, truncation, and baselap. Special operations, known to persons skilled in the art of geologic modeling, are required for introducing these stratigraphic relations into a geologic model.
Computer grids used to define zones divide the model into layers vertically, with each zone possibly having different rock properties. Within a zone, local variations in rock properties may also occur (for instance, facies changes from one depositional environment to another within a zone). Because of the need to specify different rock properties, modeling programs may introduce boundaries to separate different facies or other features within a zone. These boundaries commonly and conveniently are put in the form of polygons (i.e., ordered, closed sets of X-Y locations), but unclosed polylines or other definitions may be used. The volume enclosed by one or more of such boundaries will hereinafter be referred to as a xe2x80x9cregion.xe2x80x9d Regions typically are restricted to a single zone, but they may be defined to include two or more zones, or to be contained within a portion of a single zone. As with zones, regions often represent different geologic conditions and rock properties.
Adjustment of Geologic Interfaces in the Geologic Model
As noted above, geologic interfaces used in constructing a geologic model typically are fixed, in that their positions are not adjusted during the geologic-modeling process. There have been a few published exceptions to this practice. Roggero and Hu (xe2x80x9cGradual deformation of continuous geostatistical models for history matchingxe2x80x9d, SPE-49004, Proceedings of the 1998 Annual SPE Technical Conference, p. 221-236) developed an optimization algorithm to simultaneously condition a limited number of geologic-model parameters to historical field data. In their example, two independent geostatistical model realizations were linearly combined to produce a set of additional model realizations. Each of these realizations had a different though equally probable shape for the reservoir""s top structural surface (one of two parameters modeled). From this set of realizations, an optimum realization was identified as that having simulated production results that are most similar to actual field production data. This optimum realization was then linearly combined with a third independent model realization resulting in a second set of additional realizations, and from this set a second optimum realization was identified. This process was repeated until a convergence criterion was met, resulting in a model realization consistent with the historical field data. There are several limitations to this procedure. For example, the top structural surface is not optimally adjusted during construction of the geologic model. Rather, a set of equally probable model realizations is generated and, from this set, the optimum realization is selected. This is not necessarily an efficient process, because many model realizations may have to be constructed before an optimum realization can be identified. In addition, the resulting model is only consistent with field data; there is no attempt to ensure consistency of the structural surface with modeled rock properties or with any other data measurements or target assumptions.
Rahon et al. (xe2x80x9cIdentification of geological shapes in reservoir engineering by history matching production dataxe2x80x9d, SPE-48969, Proceedings of the 1998 Annual SPE Technical Conference, p. 139-149) similarly used field production data to modify parameters of a geologic model. In their work, structural faults and depositional-facies-object boundaries (e.g., channel boundaries) were modified to be consistent with the field production data. Faults were assumed to be vertical, spatially defined by two nodes (end-points), and assigned a fluid-transmissibility value. Channel-facies objects were assumed to have vertical boundaries, spatially defined by a limited number of nodes along the interface, and were assigned permeability values different from the surrounding non-channel facies. According to this method, a tentative model is constructed and production is simulated to generate synthetic values of production rates and pressures at well locations. These synthetic measures are compared to actual field measures, and the nodes of the faults or facies boundaries are adjusted until an objective function, measuring the difference in the real and synthetic values, is minimized. It is not clear what, if any, constraints are applied to control movement of the nodes. As with the Roggero and Hu method described above, the resulting model is only consistent with field data; there is no attempt to ensure consistency of the fault or boundary positions with modeled rock properties or with any other data measurements or target assumptions. There are no obvious constraints controlling adjustment of the nodes. Rahon et al. previously published a similar study (xe2x80x9cIdentification of geological shapes in reservoir engineering using well tests and history matchingxe2x80x9d, SPE-38656, Proceedings of the 1997 Annual SPE Technical Conference, p. 141-153), except that well test data were used to modify the parameters of the geologic model.
U.S. Pat. No. 4,679,174 describes a procedure to optimize a 2-D model of subsurface earth layers (see also, Gelfand and Larner, xe2x80x9cSeismic lithologic modelingxe2x80x9d, The Leading Edge, 1984, p. 30-35). In this procedure, a tentative 2-D geologic model is constructed that consists of layers defined by horizons, presumably interpreted from the seismic data. Additional horizons are arbitrarily inserted within these layers, creating many layers of varying thickness. Acoustic-velocity and bulk-density values are assigned at selected model control points at each horizon. Acoustic-velocity, density, and depth values are interpolated between these control points at defined locations, referred to as calculation points. These parameters at calculation points are allowed to vary over specified ranges, and synthetic seismic traces are calculated for each change in the model using a convolutional modeling process. The parameters are varied until the synthetic seismic traces are in agreement with observed seismic traces. The result is a 2-D model of subsurface earth layers that is consistent with stratal features in the seismic data.
A procedure similar to the one described in U.S. Pat. No. 4,679,174 has been published by several different authors (see e.g., Duboz et al., xe2x80x9cMoving to a layered impedence cube: advantages of 3D stratigraphic inversionxe2x80x9d, First Break, 1998, p. 311-318 and Gluck et al., xe2x80x9cRobust multichannel stratigraphic inversion of stacked dataxe2x80x9d, Developments in Geophysical Techniques Relating to Finding the Subtle Trap, Norwegian Petroleum Society, 1990). According to this procedure, a tentative 3-D geologic model is created, with stratal geometries defined by interpreted seismic horizons. Acoustic-impedance values are assigned to layers bounded by these horizons (referred to as macro layers), and impedance values may vary laterally and vertically. This continuous impedance field is sampled at regular intervals. Vertical sampling within each macro layer is defined by interpolating strata (micro layers) to adequately represent layer geometry, though not necessarily to conform to the geometries of seismic reflectors. At each sample location, parameters of impedance and seismic reflection time are assigned. These parameters are perturbed, and synthetic seismic traces are calculated for each change in the model using a convolutional modeling process. The parameters are varied until the synthetic seismic traces are in agreement with the observed traces. The a priori model is constrained in terms of impedance bounds and lateral continuity. Similar constraints are not applied to control the perturbation of seismic time at sample locations. The resulting model consists of a layer geometry that conforms to strata features in the seismic data.
In the procedures described in U.S. Pat. No. 4,679,174 and the publications by Duboz et al. and Gluck et al., surfaces within the model are adjusted while the model is being constructed. However, the resulting models are consistent only with the seismic data, and not with modeled rock properties or with any other data measurements or target assumptions. Impedance or acoustic-velocity and density values may be constrained in the model, but there are no constraints controlling the perturbation of depth or time values. Thus, the resulting product is not a geologic model of rock properties for a subsurface earth volume, but simply a forward seismic model of the layered subsurface.
From the foregoing, it can be seen that there is a need for a procedure in which the geologic interfaces within a 3-D geologic model can be adjusted during the model-building process so that the resulting model is consistent with data measurements and target assumptions for the subsurface earth volume being modeled, including available seismic data. Preferably, such a procedure should be automated so that the optimization process can be performed by a computer, resulting in a more accurate model of the subsurface earth volume of interest, but requiring negligible additional time and effort. The present invention satisfies this need.
The present invention is a process for constructing a 3-D geologic model of a subsurface earth volume containing one or more geologic interfaces. In one embodiment, the inventive process comprises the steps of (a) generating a tentative geologic model of the subsurface earth volume, the tentative geologic model comprising a three-dimensional array of contiguous model blocks, each model block having tentative values of one or more rock properties assigned thereto, the tentative geologic model containing tentative positions for the one or more geologic interfaces; (b) specifying training criteria which define the spatial attributes of geologic interfaces and the characteristics of rock properties in the subsurface earth volume; (c) calculating statistics that describe the spatial attributes of the tentative to geologic-interface positions and the characteristics of the tentative rock-property values in the tentative geologic model; and (d) comparing statistics calculated in step (c) with corresponding training criteria specified in step (b) and either (1) if the statistics do not match the training criteria within specified limits, perturbing the tentative position within the tentative geologic model of at least a portion of at least one of the geologic interfaces, updating the tentative geologic model, and repeating steps (c) and (d), or (2) if the statistics match the training criteria within the specified limits, accepting the tentative geologic model as the three-dimensional geologic model for the subsurface earth volume.
In a preferred embodiment, the process further includes the step of perturbing the tentative value of at least one rock property for at least one of the model blocks prior to updating the tentative geologic model. In this embodiment, the tentative positions within the tentative geologic model of the geologic interfaces are preferably moved as required to be consistent with the perturbed rock-property values.
Preferably, the training criteria used to assess the tentative geologic model include the match between synthetic seismic traces derived from the tentative geologic model and actual seismic data traces for the subsurface earth volume being modeled.
In the event that one or more wells have been drilled in the subsurface earth volume, then rock-property values obtained from these wells should be assigned to model blocks representing portions of the subsurface earth volume that are penetrated by the wells. Similarly, geologic-interface locations obtained from wells should be inserted into the model at positions corresponding to their locations in the wells. Preferably, these rock-property values and geologic-interface positions at the wells are accepted as correct, and are not subject to perturbation.